PrecalculusMrs. Spatola
Name______Date______
Check for understanding quiz
a)Find the domain of the function
b)Find the x and y coordinates of any holes in the graph of the function.
c)Write the equation of any vertical asymptotes.
d)Describe the behavior of the graph as x approaches the asymptote from the left and right. (create a table to observe where the graph is going)
x→ / f(x) / x→ / f(x)Turn the page over
Write your answer to Homework Question #1 from lesson #16
i)
ii)
iii)
iv) (you do not have to rewrite your table, just describe the shape of the graph)
SWBAT find x & y-intercepts of rational functions.
(Lesson 17 - 3-4)
Finding y-intercepts
If a function - any function is defined at x = 0, then it has a y-intercept; if it is not defined at x = 0, then it does not have a y-intercept. Rational functions, of course, may or may not be defined at zero.
1)For each of the following rational functions, determine whether the function has a y-intercept.
a)If it has a y-intercept, find the location of the y-intercept.
b)If it does not have a y-intercept, determine if it has a hole on the
y-axis or if it has a vertical asymptote at x = 0.
a)
b)
c)
d)
Finding x-intercepts
2)If the equation f(x) = 0 has one or more real roots, where f is any function then the graph of f has an x-intercept at each real root. Like polynomials, rational functions may or may not have real zeros.
- Find the domain of the function.
- Find all the real zeros of the numerator. These are the candidates for the x-intercepts.
- Test each zero. If the zero is in the domain, then it is an x-intercept. Otherwise, it is not.
a)
b)
c)
d)
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